1 of 8 0-day streak

Mixed probability applications with the normal distribution

Question 1 of 8

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Apply the stated distribution to the repeated process

Let X be the volume, in millilitres, recorded for one filled container

The distribution is \(X\sim N\left(144,400\right)\)

Use the following condition to classify each trial as a success or a failure

A success is recorded when \(X<164\)

The process is repeated for \(7\) independent trials, with the same normal model used for each trial

Let \(Y\) be the number of successes in the \(7\) trials. The required event is \(Y=5\)

Use the one-trial success probability from the normal model as the probability for the second model

(a)1 mark

Which probability model should be used for the number of successes?

Use the boundary's standard score, rather than the normal area, as the binomial success probability

The count of successes should be modelled by a binomial distribution after the normal step

(b)1 mark

Find the probability that one trial is a success. Give the answer to 2 decimal places

Probability for one success Format: 2 d.p.

Let \(Y\) be the number of successes in the \(7\) trials. The required event is \(Y=5\)

Choose the calculation that matches the requested binomial quantity

Add terms for several success counts

Use the one binomial term for exactly 5 successes

(d)1 mark

Let \(Y\) be the number of successes in the \(7\) trials. The required event is \(Y=5\)

Find the probability of exactly the stated number of successes. Give the answer to 4 decimal places

Binomial probability Format: 4 d.p.